Magnetic Anisotropy and Field-induced Slow Relaxation of Magnetization in Tetracoordinate CoII Compound [Co(CH₃-im)₂Cl₂].

Static and dynamic magnetic properties of the tetracoordinate CoII complex [Co(CH3-im)2Cl2], (1, CH3-im = N-methyl-imidazole), studied using thorough analyses of magnetometry, and High-Frequency and -Field EPR (HFEPR) measurements, are reported. The study was supported by ab initio complete active space self-consistent field (CASSCF) calculations. It has been revealed that 1 possesses a large magnetic anisotropy with a large rhombicity (magnetometry: D = -13.5 cm-1, E/D = 0.33; HFEPR: D = -14.5(1) cm-1, E/D = 0.16(1)). These experimental results agree well with the theoretical calculations (D = -11.2 cm-1, E/D = 0.18). Furthermore, it has been revealed that 1 behaves as a field-induced single-ion magnet with a relatively large spin-reversal barrier (Ueff = 33.5 K). The influence of the Cl-Co-Cl angle on magnetic anisotropy parameters was evaluated using the CASSCF calculations.

1. Introduction

Current ipan class="Chemical">nterest in molecular compounds exhibiting magnetic blocking on a single molecule, so called pan> class="Gene">single-molecule magnets (SMMs), lies in their potential practical applications in quantum computing or magnetic memories with a high density of storage [1]. The key parameter influencing static and dynamic magnetic properties of SMMs is represented by magnetic anisotropy, which manifests itself as a preferred direction of the spin, which may not be aligned with an external magnetic field, as promoted by the Zeeman Effect [2]. Two basic situations can be distinguished within the spin Hamiltonian formalism and described by the zero-field splitting (ZFS) parameters D (axial) and E (rhombic): (a) if the magnetization of the molecule exhibits a directional character, it is classified as uniaxial, containing an easy axis (D < 0); (b) if the character of magnetization is planar, the anisotropy is called easy-plane (D > 0) [3]. The value of the rhombic parameter must lie in the interval of E/D = 0−1/3 where the larger limiting value is considered as perfect rhombicity at which the sign of the D parameter cannot be determined experimentally. Furthermore, if D > 0 and if anisotropy is approaching perfect rhombicity, then magnetization is not of an easy-plane type anymore and it is strongly directional, but not along the z-axis. On the other hand, the magnetization of molecules with D < 0 stays axial even at E/D = 1/3 (Figure 1 left). The reason for this lies in the choice of the coordinate system for the components of the D-tensor (D). When the ideal rhombicity is achieved (or overpassed), the change of the canonical order of the D-tensor components occurs (for more detailed explanation, see the work of M. Atanasov et al. [4]). This is also reflected in a change of the magnetization axes without a change of the overall (orientationally averaged) magnetic properties (Figure 1 right).

Figure 1

(a) The 3D visualization of the molar magnetization calculated at T = 2 K and B = 3 T for S = 3/2 with various D and E parameters as indicated in the plot. (b) The effective magnetic moment with molar magnetization in the inset (B = 0.1 T) and the isothermal magnetization at T = 2 K calculated for D = −50 cm−1, E/D = 1/3 (top) and D = +50 cm−1, E/D = 1/3 (bottom).

The above mentiopan class="Chemical">ned considerations have significant consequenpan>ces with respect to a definpan>ition of the pan> class="Gene">spin reversal barrier (Ueff) of SMMs. The well-established relationship defines Ueff for integer spins (S) as Ueff = ǀDǀ × S2 and for non-integer spins as Ueff = ǀDǀ × (S2 − 1/4). It is clear that if one wants to increase the value of Ueff, there are only two possibilities: to increase the ground state spin or the absolute value of D. Previously, it was shown that increasing of total S by synthesizing large polynuclear clusters of paramagnetic metal atoms does not lead to increasing of Ueff. Furthermore, this strategy is not straightforward either from the synthetic or from theoretical point of view [5,6]. The other strategy involves deliberate tuning of magnetic anisotropy. Again, this is not straightforward for polynuclear complexes due to different mutual orientations of local D-tensor components depending on several conditions (e.g., cluster topology, differences in compositions of the coordination polyhedra implying different types of anisotropy) and interplay between the magnetic coupling and anisotropy [7]. Nevertheless, if we consider a special category of SMMs with one paramagnetic center, so called single-ion magnets (SIMs), then the deliberate modulation of the magnetic anisotropy is easier and depends reasonably on the topology and donor atom constitution of the coordination polyhedron [2]. Up to now, several correlations on the relationship between a structure and anisotropy parameters have been reported, namely for tetracoordinate [8,9], pentacoordinate [10,11], hexacoordinate NiII and CoII compounds [12,13], tetracoordinate FeII compounds [14] and penta and hexacoordinate MnIII compounds [15,16]. From these, the largest number of complexes exhibiting slow-relaxation of magnetization belongs undoubtedly to the group of tetracoordinate CoII compounds, which we have chosen as an object of the present study.

The ground electropan class="Chemical">nic state in tetracoordinate CoII complexes (with S = 3/2) with the ideal Td geometry is 4A2 (the same for the C2v poinpan>t group), but with lowerinpan>g of the symmetry it might chanpan>ge to 4B1(D2d), 4A’’(CS) anpan>d 4A(C1). The ground state is split by ZFS inpan> two Kramers doublets ǀ3/2,±3/2> anpan>d ǀ3/2,±1/2> anpan>d thepan> class="Chemical">se two levels are separated by an energy difference equal to 2D. If the rhombic anisotropy is present, the distance between the Kramers doublets increases by 2√(D2 + 3E2). Usually, the tetracoordinate CoII compounds of the composition [Co(LN/P)2(L1)2], (where LN/P = a monodentate N/P-n class="Species">donor ligand, L1 = halogenido or pseudohalogenido ligands), adopt values of D parameters ranging from −14 to +6 cm−1 [17]. It must be noted that much larger values of D were observed for compounds involving monodentate ligands with soft donor atoms such as S or Se [18], bidentate N-donor ligands [19], and bidentate S/Se-donor ligands [20,21]. The aforementioned correlation [9] on the anisotropy of the [Co(LN/P)2(L1)2] compounds involves N/P-Co-N/P (α) and N/X-Co-N/X angles (β, N or X are the donor atoms from the L1 ligands) and it reads: δ = 2αTd – (α + β), where αTd is the angle of the ideal tetrahedron (109.5°). More negative/positive δ should lead to more negative/positive D. Thus, we performed a search in the CSD database (version 5.37 updated to May 2016) [22] for interesting candidates within the group of [Co(LN)2(Cl)2] compounds, which are readily synthetically available. Furthermore, in the previous works [9,17,23,24,25] the influence of the change in the α angle on D was well documented and therefore, we decided to study a compound with a large β angle, which should also lead to negative δ and D. From the CSD search we know that the average and median β values are both larger (114.1° and 114.4°) than the ideal tetrahedral angle. Therefore, we decided to choose to study the compound [Co(CH3-im)2Cl2], (1, CH3-im = N-methyl-imidazole), which possesses a relatively large β angle (117.9°) and to study its static and dynamic magnetic properties by Superconducting Quantum Interference Device (SQUID) magnetometry and High-Frequency and -Field EPR (HFEPR). Furthermore, we performed an extensive computational study of its electronic structure by CASSCF calculations and we studied the influence of widening of the β angle on the D and E parameters.

2. Results

2.1. Crystal Structure

The crystal structure of the title compound 1 was reported ipan class="Chemical">n the year 2000 by S. Mukerjee et al. [26], but herein we will focus on the structural details, which might be important for the analysis of the magnetic behavior of this compound. The complex molecule in 1 is composed of two CH3-im anpan>d two Cl− liganpan>ds coordinpan>ated to the pan> class="Gene">CoII atom. As a result, the complex is tetracoordinate with symmetry of the coordination polyhedron close to C2v (Figure 2). The Co−N bonds are significantly shorter than the Co–Cl ones (in Å): d(Co−N) = 2.004(3) and 2.008(3), d(Co−Cl) = 2.2479(9) 2.2509(8). The Cl−Co−Cl angle is much wider than the N−Co−N one: <(Cl−Co−Cl) = 117.94(4)° and <(N−Co−N) = 110.6(1)°. Thus, the δ parameter is negative in this case (−9.5°).

Figure 2

Molecular structure of 1. Selected bond lengths (in Å) and angles (in °): d(Co1−N1) = 2.004(3), d(Co1−N3) = 2.008(3), d(Co1−Cl1) = 2.2509(8), d(Co1−Cl2) = 2.2479(9), <(Cl1−Co1−Cl2, α angle) = 117.94(4), <(N1−Co−N3, β angle) = 110.6(1), <(N1−Co−Cl2) = 103.42(8), <(N1−Co−Cl1) = 111.08(8), <(N3−Co−Cl1) = 105.52(8), <(N3−Co−Cl2) = 108.26(9). The X-ray data were adapted from CSD refcode XIWKIX [22].

The crystal structure of 1 does not copan class="Chemical">ntain any significant non-covalent contacts, only very weak C–H···Cl and C–H···π interactions are present. Furthermore, the shortest inpan>termolecular Co···Co distanpan>ce is 6.656(1) Å anpan>d thus, no mediation of magnpan>etic exchanpan>ge through non-covalenpan>t inpan>teractions or dipolar inpan>teraction canpan> be expected. The phapan> class="Chemical">se identity of 1 was confirmed using powder X-ray diffraction and the observed powder diffraction pattern was compared to that calculated from the n class="Gene">single-crystal data (Supplementary Materials, Figure S1).

2.2. Static Magnetic Properties

Temperature (1.9–300 K) and field (0–9 T) depepan class="Chemical">ndent magnetic data obtained by a physical property measurement system (PPMS) magnetometer are shown in Figure 3. The effective magnetic moment (μeff) at room temperature adopts the value of 4.4 μB. This value is significantly higher than the spin-only value for S = 3/2 anpan>d g = 2.0 (μeff/μB = 3.87) which directly inpan>dicates considerable contribution of a pan> class="Gene">spin-orbit coupling to the ground state. Furthermore, μeff/μB starts to decrease on cooling below 40 K and it reaches the value of 3.5 at 1.9 K. From the field dependent measurements of molar magnetization it is clear that the isothermal magnetizations do not saturate to the value Mmol/NAμB = g × S. With respect to the mononuclear character of 1 and the absence of the intermolecular interactions capable of mediating magnetic exchange, such deviations from the ideal paramagnet behaviour cannot be explained by any other reasons than ZFS.

Figure 3

The magnetic data for 1 depicted as temperature dependence of the effective magnetic moment calculated from the molar magnetization measured at B = 0.1 T shown in the inset and reduced magnetization data measured at T = 2 and 5 K. Experimental data are depicted as empty circles, fitted data are shown as red lines. (a) The best fit for negative D: g = 2.287, D = −13.5 cm−1, E/D = 0.33 and χTIP = 5.18 × 10−9 m3·mol−1. (b) The best fit for positive D: g = 2.298, D = 14.3 cm−1, E/D = 0.30 and χTIP = 5.04 × 10−9 m3·mol−1. Blue lines correspond to magnetic data derived from CASSCF/NEVPT2 calculation.

Thus, in order to apan class="Chemical">nalyze the magnetic properties of 1, we postulated the spin Hamiltonianpan> for the monpan>omeric complex includinpan>g axial anpan>d rhombic terms of ZFS, anpan>d Zeemanpan> term, where a definpan>es the orienpan>tation of the magnpan>etic field vector inpan> polar coordinpan>ates as B = B(pan> class="Gene">sin θ cos ϕ, sin θ sin ϕ, cos θ). The final calculated molar magnetization was calculated as an integral average in order to properly simulate the powder sample signal.

Both, temperature- and field-depepan class="Chemical">ndent magnetic data were fitted simultaneously in order to find a reliable set of parameters. Firstly, the alternpan>ative with the negative D value was evaluated anpan>d the resultinpan>g fit is relatively good (Figure 3a) for D = −13.5 cm−1, E/D = 0.33, g = 2.287 anpan>d χTIP = 5.18 × 10−9 m3·mol−1, where χTIP stanpan>ds for the conpan>tribution of temperature-inpan>depenpan>denpan>t paramagnpan>etism [27]. Secondly, the positive D value was restrained in the fitting procedure and this resulted again in a very good fit, but with a little lower rhombicity: D = 14.3 cm−1, E/D = 0.30, g = 2.298 and χTIP = 5.04 × 10−9 m3·mol−1 (Figure 3b). Nevertheless, from the magnetic measurements it is clear that 1 has large rhombicity and we are not able to determine the sign of the D parameter unambiguously.

2.3. HFEPR

For a more accurate determinatiopan class="Chemical">n of the ZFS parameters we employed (HFEPR). Thus, spectra of pressed powder pellets were obtainpan>ed at variable temperatures (from 8 to 40 K) anpan>d variable frequencies (from 100 to 500 GHz). The spectra were simulated on the basis of the pan> class="Gene">spin Hamiltonian in the Equation (1) and we were able to reproduce all the dominant features observed in the simulations (Figure 4).

Figure 4

HFEPR frequency dependence of 1 at 40 K. Colored lines represent experimental data, while grey lines represent the simulated spectra.

From the simulations, we foupan class="Chemical">nd that the second ranpan>k axial ZFS parameter D = −14.5 ± 0.1 cm−1 is negative anpan>d similar inpan> magnpan>itude to that obtainpan>ed from the PPMS measuremenpan>ts. However, the rhombicity is substanpan>tially lower: E/D = 0.16 ± 0.01. The g factor is anpan>isotropan> class="Chemical">pic with gx = 2.21 ± 0.01, gy = 2.18 ± 0.01 and gz = 2.40 ± 0.01. Although most of the observed signals come from intradoublet transitions, the sign of D can be assigned unambiguously mainly due to the variable temperature measurements (Figures S9 and S10), which cannot be reproduced with a positive D. Further HFEPR measurements and analyses can be found in Supplementary Materials (Figures S2–S11).

2.4. CASSCF Calculations

In order to support the apan class="Chemical">nalysis of the experimental data computationally we performed the complete active space self-consistenpan>t field (CASSCF) calculations complemenpan>ted by N-electron valenpan>ce pan> class="Chemical">second order perturbation theory (NEVPT2) using an ORCA 3.0 computational package [28]. The relativistic effects were included with a zero order regular approximation (ZORA) and scalar relativistic contracted version of def2-TZVP(-f) basis functions, as described in the Experimental Section 4.2.2. The n class="Gene">spin Hamiltonian parameters were extracted with the help of the effective Hamiltonian theory. The resulting ZFS parameters for S = 3/2 are a little lower than those obtained from the HFEPR data: D = −11.2 cm−1, E/D = 0.18 (implying thus Ueff = 33.8 K/23.5 cm−1). The calculations also showed anisotropy of the g-tensor components (2.191, 2.240, 2.357, gav = 2.263), which agrees nicely with the results obtained by HFEPR. We also employed the respective ab initio CASSCF/NEVPT2 spin-orbit coupling, orbital and spin angular momentum matrices to calculate all 120 energy levels for any orientation of magnetic field , followed by integral calculation of both temperature- and field-dependent magnetization data, which are in good agreement with the experimental data (Figure 3). Moreover, both lowest Kramers doublets (KD) were analyzed with the spin Hamiltonian for the effective spin Seff = 1/2, which resulted in the g-tensor components gKD1 = (1.051, 1.277, 6.850) and gKD2 = (2.152, 3.200, 5.430). Evidently, the lowest Kramers doublet has the axial type of the magnetic anisotropy, whereas the second Kramers doublet has a plane type of the magnetic anisotropy. Indeed, the easy axis type of the magnetic anisotropy is also clearly visible in Figure 5, where the 3D plot of the molar magnetization is overlaid over the molecular structure of 1 with the principle axes of the D-tensor.

Figure 5

The CASSCF/NEVPT2 calculated principal axes of the D-tensor labeled DX (pink), DY (green), DZ (blue) visualized together with molecular structure of 1 and overlaid with calculated molar magnetization (B = 3 T, T = 2 K).

2.5. Dynamic Magnetic Properties

The AC susceptibility data measured in the zero static magpan class="Chemical">netic field showed no significant out-of-phase susceptibility signpan>al (Supplemenpan>tary Materials, Figure pan> class="Gene">S12), but the field dependent measurement at T = 1.9 K confirmed field-induced slow relaxation of magnetization in 1 with a maximum at 0.2 T. This confirmed that 1 exhibits field-induced slow-relaxation of magnetization. Therefore, the AC data were collected at non-zero static field B = 0.2 T for various frequencies of small AC field as depicted in Figure 6. From this measurement it is obvious that the peak maxima are frequency dependent and 1 can be classified as field-induced SIM. Therefore, the analysis of the dynamic magnetic properties was done using the one-component Debye model:

Figure 6

(a) In-phase χreal (left) and out-of-phase χimag (right) molar susceptibilities for 1 at the applied external field Bdc = 0.2 T. Lines serve as guides to the eyes. (b): Frequency dependence of in-phase χreal (left) and out-of-phase χimag (right) molar susceptibilities for 1 at Bdc = 0.2 T. Full points—experimental data, full lines—fitted data using Equation (5).

As a result a n class="Chemical">sepan>t of parameters containpan>inpan>g isothermal (χT) anpan>d adiabatic (χS) susceptibilities, relaxation times (τ) anpan>d distribution parameters (α) was obtainpan>ed (Supplemenpan>tary Materials, Table S1). Thenpan>, the Arganpan>d (Cole–Cole) plot (Figure 7) was constructed anpan>d upan> class="Gene">sing the Arrhenius expression for the temperature dependence of relaxation time resulted in τ0 = 2.11(0.95) × 10−9 s−1 and the spin reversal barrier Ueff = 33.5(1.2) K/23.3(0.8) cm−1 (Figure 7). Such derived value is slightly lower than the theoretical value of Ueff = 43.3 K/30.1 cm−1 estimated with D = −14.5 cm−1, E/D = 0.16, where the D and E values were determined by HFEPR. The reason why Ueff derived from the AC susceptibility data is smaller than theoretically predicted is that other relaxation processes than the Orbach one could also be present. However, the discrepancy can also be caused by the fact that with the Equation (5) only data having the maxima on the imaginary part of susceptibility are analyzed (T ≤ 3.1 K), and the non-zero values are already observed at ≈ 4 K. Therefore, we analysed these high temperature data for the highest frequencies with a simplified model derived under the assumption that the adiabatic susceptibility is usually approaching zero in the single-molecule magnets [29]

Figure 7

(a) Argand (Cole–Cole) plot and fit (b) of resulting relaxation times according to Arrhenius equation (red line).

As a result, we obtained papan class="Chemical">n class="Chemical">sets of the followinpan>g parameters: τ0 = 1.8 × 10−10, Ueff = 29.8 cm−1 (42.9 K) for f = 1488.1 Hz, τ0 = 3.1× 10−10, Ueff = 28.5 cm−1 (41.0 K) for f = 715.6 Hz, τ0 = 4.2 × 10−10, Ueff = 28.2 cm−1 (40.6 K) for f = 344.7 Hz in Figure S13 (Supplemenpan>tary Materials). The slight variation of the obtainpan>ed parameters canpan> be due to omittinpan>g the distribution of relaxation processes (parameter a in the Equation (5)). In this case Ueff is very close to the theoretical estimate ≈ 45 K.

3. Discussion

First, we will compare the results we obtained with the characteristics of the previously reported tetracoordipan class="Chemical">nate compounds of the [Co(LN/P)2(L1)2] and [Co(LN/P)(L1)2] types. The values of the selected magnpan>etic anpan>d structural parameters are listed inpan> Table 1. Detailed inpan>spection of the data anpan>d comparison with the correlation propopan> class="Chemical">sed by Boča and co-workers [9] show (Figure 8) that the relationship between δ and D is not linear, even if it is obvious that the compounds with negative δ tend to possess negative D and vice versa.

Table 1

Selected magnetic and structural parameters of [Co(LN/P)2(L1)2] and [Co(LN/P)(L1)2] compounds.

Compound a	D	E/D	BDC/T b	Ueff/K	τ0	α (°)	β (°)	δ (°)	Ref.
1	−13.5	0.33	0.2	33.5	2.1 × 10−9	110.6	117.9	−9.5	This work
{CoN2Cl2}	−14.5 c	0.16 c
[Co(qu)2(NCS)2] {CoN’2N’’2}	+6.2	0	-	-	-	104.5	108.3	+6.2	[9]
[Co(qu)2Cl2] {CoN2Cl2}	−5.2	0	-	-	-	107.2	113.4	−1.6	[9]
[Co(qu)2I2] {CoN2I2}	+9.2	0	-	-	-	101.8	109.7	+7.5	[9]
[Co(pic)2Cl2] {CoN2Cl2}	−5.3	0	-	-	-	107.4	121.4	−9.8	[9]
[Co(PPh3)2Cl2] {CoP2Cl2}	−11.8	0	0.1	37.1	1.2 × 10−9	115.9	117.1	−14.0	[30]
	−14.8 c
[Co(PPh3)2Br2] {CoP2Br2}	−13.0	0	0.1	37.3	9.4 × 10−11	117.4	115.2	−13.6	[31]
[Co(PPh3)2I2] {CoP2I2}	−36.9	0	0.1	30.6	4.7 × 10−10	108.3	111.4	−0.7	[32]
[Co(menim)2Cl2] {CoN2Cl2}	+11.4	0.01	-	-	-	102.4	111.0	+5.6	[33]
	+11.4 c	0.21 c
[Co(ampyr)2Cl2] {CoN2Cl2}	−10.0	0.24	-	-	-	114.5	110.4	−5.9	[33]
	−8.0 c	0.28 c
[Co(bzi)2Cl2] {CoN2Cl2}	+2.2	0.22	-	-	-	106.2	112.0	+0.8	[33]
	±3.3 c	0.28 c
[Co(cyt)2Cl2] {CoN2Cl2}	−5.2	0.10	-	-	-	110.4	103.4	+5.2	[33]
	−4.3 c	0.05 c
[Co(im)2Cl2] {CoN2Cl2}	+5.7	0.05	-	-	-	105.3	111.2	+2.5	[33]
	+9.2 c	0.10 c
[Co(PPh3)2(NCS)2] {CoN2P2}	−9.4	0	0.2	-	-	113.4	114.3	−8.7	[34]
[Co(bzi)2(NCS)2] {CoN’2N’’2}	−10.1	0	0.2	21.4	1.2 × 10−8	115.7	109.6	−6.3	[17]
[Co(biq)Cl2] {CoN2Cl2}	+10.5	0	0.2	42.6	1.9 × 10−10	81.7	117.4	+19.9	[23]
[Co(biq)Br2] {CoN2Br2}	+12.5	0	0.2	39.6	1.2 × 10−10	81.9	117.9	+19.2	[23]
[Co(biq)I2] {CoN2I2}	+10.3	0	0.2	57.0	3.2 × 10−13	81.9	118.3	+18.8	[23]
[Co(dmph)Br2]	+11.7	0	0.1	22.8	3.7 × 10−10	83.1	115.9	+20.0	[35]
{CoP2Cl2}
[Co(bcp)Cl2]	−6.6	0	0.2	47.8	1.3 × 10−11	81.6	120.0	+17.4	[36]
{CoN2Cl2}
[Co(bcp)Br2]	−6.7	0	-	-	-	81.9	120.8	+16.3	[36]
{CoN2Br2}
[Co(bcp)I2]	-7.0	0	-	-	-	82.1	121.7	+15.2	[36]
{CoN2I2}

Abbreviations: qu = quinoline, pic = γ-picoline, PPh3 = triphenylphosphane, bzi = benzimidazole, biq = 2,2’-biquinoline, dmph = 2,9-dimethyl-1,10-phenanthroline, im = imidazole, menim = dimethylnitroimidazole, ampyr = aminopyrimidine, cyt = cytosine, bcp = bathocuproine. static magnetic field used in AC measurements of slow-relaxation of magnetization, and E determined by HFEPR.

Figure 8

A plot of the possible magneto-structural relationship between D and δ for tetracoordinate CoII complexes. The D-values are taken from the analysis of the magnetic data.

Next, as we mepan class="Chemical">ntioned in the introduction, the X–Co–X angle plays an important role in the above mentioned magneto-structural correlation. Furthermore, in this study, we have chosen the compounpan>d [pan> class="Chemical">Co(CH3-im)2Cl2] due to its relatively large Cl–Co–Cl angle (117.9°). From the structural data listed in Table 1, one can see that the X–Co–X angles are from a less extensive range of values (from 115.9° to 121.9°) in compounds with bidentate chelating ligands, while compounds with monodentate N/P-donor ligands adopt a much more variable range of the X–Co–X angles (from 108.3° to 121.4°). Therefore, we decided to explore the influence of the Cl–Co–Cl l angle on the ZFS parameters alone using the partially constrained geometry of the [Co(CH3-im)2Cl2] molecule with the Cl–Co–Cl angle adopting values close to the latter of the above-mentioned ranges. Thus, the N–Co–N angle was constrained to the value determined from the single-crystal X-ray diffraction experiment (110.6°) and the Cl–Co–Cl angle was varied from 109.5° to a maximal value of 127°. The molecular structure (for each Cl–Co–Cl angle) was optimized by DFT using PBE/ZORA/def2-TZVP(-f) including also dispersion correction (D3BJ) (see Section 4.2.2). As a result, we obtained a set of [Co(CH3-im)2Cl2] optimized molecular geometries with different Cl–Co–Cl angles and for each of them the CASSCF/NEVPT2 calculation was performed to deduce information about the D-tensors. The results of these calculations are shown in Figure 9.

Figure 9

The effect of the Cl–Co–Cl angle on the ZFS parameters calculated with CASSCF/NEVPT2 with molecular geometries optimized by DFT.

It is clear that the change of the papan class="Chemical">n class="Chemical">Cl-Co-Cl anpan>gle in the ranpan>ge from 109.5° to 123 has no signpan>ificanpan>t inpan>fluenpan>ce on the D parameter, which is negative with a value clopan> class="Chemical">se to −10.5 cm−1. Remarkably, in this region of the Cl-Co-Cl angle we see a dramatic increase in the rhombicity from E/D = 0.03 at 112° to almost perfect rhombicity (E/D = 0.32) at 124°. As a result, the change in the sign of the D parameter (Figure 9) is observed: D(at 124°) = 11.1 cm−1.. To sum up, no significant influence of the widening of the Cl-Co-Cl angle alone on the D value was predicted by the computational methods. On the other hand, the rhombicity parameter is strongly dependent on such widening to the extent that even a change of the D-sign at angles wider than 124° was predicted. Furthermore, it is evident that for the optimized geometries, the D-parameter does not correlate with the structural parameter δ (Figure 9). This, together with the above-mentioned discrepancy found for a set of magnetic and structural data for [Co(LN/P)2(L1)2] complexes, simply reveals that the previously proposed magneto-structural correlation [9] cannot cover all structural nuances in tetracoordinate CoII complexes.

4. Materials and Methods

4.1. Materials

All the starting chemicals were of analytical reagent grade and were un class="Chemical">sed as received. All the chemicals were purchapan> class="Chemical">sed from commercial sources (Sigma Aldrich, St. Louis, MO, USA).

Preparation of [Co(CH3-im)2Cl2]

A solution of papan class="Chemical">n class="Chemical">CoCl2 (1 mmol, inpan> 15 mL of n class="Chemical">methanol) was slowly added to a solution of n class="Chemical">N-methyl-imidazole (2 mmol, in 15 mL of methanol) during stirring. The solution immediately turned dark blue. It was stirred with heating for next 15 min and then it was filtered through a paper filter. After two days blue crystals formed and they were filtered off, washed with methanol and diethyether, dried and stored in a vacuum desiccator. Yield: 58%. Elem. anal. Calcd (%) for C8H12Cl2Co1N4: C, 32.68; H, 4.11; N, 19.05. Found: C, 32.77; H, 4.13; N, 18.75.

4.2. Methods

4.2.1. General Methods

Elemental apan class="Chemical">nalysis (CHN) was performed on a FLASH 2000 CHN Analyser (ThermoFisher Scienpan>tific, Waltham, MA, USA). The static magnpan>etic data were measured on powdered samples prespan> class="Chemical">sed into pellets using a PPMS Dynacool (Quantum Design Inc., San Diego, CA, USA). The dynamic magnetic data were measured on powdered samples pressed into pellets stabilized by eicosane using a MPMS XL-7 Quantum Design SQUID magnetometer (Quantum Design Inc., San Diego, CA, USA). The experimental data were corrected for the diamagnetism of the constituent atoms by using Pascal's constants. The X-ray powder diffraction patterns were recorded on a Mini-Flex600 (Rigaku, Tokyo, Japan) instrument equipped with the Bragg–Brentano geometry, and with iron-filtered Cu Kα1,2 radiation. High-frequency EPR spectra were recorded on a home-built spectrometer. Its radiation source is a 0–20 GHz signal generator (Anritsu or VDI) in combination with an amplifier–multiplier chain (VDI) to obtain the required frequencies (80–1100 GHz). It features a quasi-optical bridge (Thomas Keating, Billingshurst, UK) and induction mode detection. The detector is a QMC Instruments magnetically tuned InSb hot electron bolometer. The sample is located in an Oxford Instruments 15/17 T cryomagnet equipped with a variable temperature insert (1.5–300 K). The spectrometer control program was written in LabView. The spectra were obtained on powdered samples pressed into pellets. A typical linewidth of a hyperfine-split Co line is around 3.4 mT, as can be seen for example in [37]. Due to inhomogeneous broadening of the lines (the narrowest of about 100 mT) in our spectra, the hyperfine interaction from the cobalt nucleus remained unresolved. HFEPR spectra were analyzed using the EasySpin [38] toolbox for MATLAB software.

4.2.2. Theoretical Methods

All theoretical calculations were performed with the ORCA 3.0 computatiopan class="Chemical">nal package [28]. All the calculations employed the scalar relativistic contracted version of def2-TZVP(-f) basis functions [39] together with the zero-order regular approximation (ZORA) [40,41]. The ZFS and g tensors were calculated by using pan> class="Chemical">self-consistent field (SA-CASSCF) wave functions [42] complemented by N-electron valence second-order perturbation theory (NEVPT2) [43]. The active space of the CASSCF calculation was set to five d-orbitals of CoII (CAS(7,5)). The ZFS parameters, based on dominant spin−orbit coupling contributions from excited states, were calculated through quasi-degenerate perturbation theory (QDPT) [44], in which approximations to the Breit–Pauli form of the spin-orbit coupling operator (SOMF approximation) [45] and the effective Hamiltonian theory [46] were utilized. The contributions of excited states to the ZFS terms are tabulated in Table S2 and the energy levels of ligand field multiplets are listed in Table S3. The DFT calculations were based on PBE functional [47] and dispersion correction (D3BJ) was also included [48].